Question

Package Newton’s method for approximating square roots (Case Study 3.6) in a function named newton. This function expects the input number as an argument and returns the estimate of its square root. The script should also include a main function that allows the user to compute square roots of inputs until she presses the enter/return key.

Answer 1

Answer:

import math

#Initialize tolerance

tolerance = 0.000001

def newton(x):

   """ Returns the square root of x """

   #Performs the successive approximations

   estimate = 1.0

   while True:

       estimate = (estimate + x / estimate) / 2

       difference = abs(x - estimate ** 2)

       if difference <= tolerance:     # Break out of loop if difference is less than tolerance

           break            

       return estimate     # While the difference value is > TOLERANCE, the process continues

def main():

   """Allows the user to obtain square roots."""

   while True:

       #Receive the input number from the user

       x = input("Enter a positive number or enter/return to quit: ")

       if x == "":     #if user presses "Enter" then exit the program

           break       # Otherwise, continue the process of allowing new numbers

       x = float(x)

       #Output the result

       print("The programs estimate of the square root of ", x, "is ", round(newton(x),2))

       print("Python's estimate: ", math.sqrt(x))

main()